{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 2: Drawing with 2D Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Picturing 2D Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "from vector_drawing import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x365.538 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dino_vectors = [(6,4), (3,1), (1,2), (-1,5), (-2,5), (-3,4), (-4,4),\n",
    "    (-5,3), (-5,2), (-2,2), (-5,1), (-4,0), (-2,1), (-1,0), (0,-3),\n",
    "    (-1,-4), (1,-4), (2,-3), (1,-2), (3,-1), (5,1)\n",
    "]\n",
    "\n",
    "draw(\n",
    "    Points(*dino_vectors)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x365.538 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*dino_vectors),\n",
    "    Segment((6,4),(3,1))\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Draw the dinosaur with the dots connected by constructing a `Polygon` object with the `dino_vectors` as its vertices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x365.538 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*dino_vectors),\n",
    "    Polygon(*dino_vectors)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE** Draw the vectors `[(x,x**2) for x in range(-10,11)]` as points (dots) using the draw function.  What is the result?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*[(x,x**2) for x in range(-10,11)]),\n",
    "    grid=(1,10),\n",
    "    nice_aspect_ratio=False # don't require x scale to match y scale\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plane Vector Arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(v1,v2):\n",
    "    return (v1[0] + v2[0], v1[1] + v2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dino_vectors2 = [add((-1.5,-2.5), v) for v in dino_vectors]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x403.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*dino_vectors, color=blue),\n",
    "    Polygon(*dino_vectors, color=blue),\n",
    "    Points(*dino_vectors2, color=red),\n",
    "    Polygon(*dino_vectors2, color=red)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x403.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "arrows = [Segment(tip,tail,color=black) for (tip,tail) in\n",
    "         zip(dino_vectors2, dino_vectors)]\n",
    "draw(\n",
    "    Points(*dino_vectors, color=blue),\n",
    "    Polygon(*dino_vectors, color=blue),\n",
    "    Points(*dino_vectors2, color=red),\n",
    "    Polygon(*dino_vectors2, color=red),\n",
    "    *arrows\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vector components and lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def length(v):\n",
    "    return sqrt(v[0]**2 + v[1]**2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Subtraction, displacement, and distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points((2,2), (-1,3)),\n",
    "    Segment((2,2), (-1,3), color=red)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MINI-PROJECT:** You can add any number of vectors together by summing all of their $x$-coordinates and all of their $y$-coordinates.  For instance the four-fold sum (1,2) + (2,4) + (3,6) + (4,8) has $x$-component 1 + 2 + 3 + 4 = 10 and $y$-component 2 + 4 + 6 + 8 = 20, making the result (10,20).  Implement a revised add function that takes any number of vectors as arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(*vectors):\n",
    "    return (sum([v[0] for v in vectors]), sum([v[1] for v in vectors]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Write a function translate(translation, vectors) that takes in a translation vector and a list of input vectors and returns a list of the input vectors all translated by the translation vector. For instance, `translate((1,1), [(0,0), (0,1,), (-3,-3)])` should return `[(1,1),(1,2),(-2,-2)]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 1), (1, 2), (-2, -2)]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def translate(translation, vectors):\n",
    "    return [add(translation, v) for v in vectors]\n",
    "\n",
    "translate((1,1), [(0,0), (0,1,), (-3,-3)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MINI-PROJECT:** Write a Python function using vector addition to show 100 simultaneous and non-overlapping copies of the dinosaur.  This shows the power of computer graphics: imagine how tedious it would be to specify all 2,100 coordinate pairs by hand!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hundred_dinos():\n",
    "    translations = [(12*x,10*y) \n",
    "                    for x in range(-5,5) \n",
    "                    for y in range(-5,5)]\n",
    "    dinos = [Polygon(*translate(t, dino_vectors),color=blue)\n",
    "                for t in translations]\n",
    "    draw(*dinos, grid=None, axes=None, origin=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x359.395 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hundred_dinos()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** What vector in the dino_vectors list has the longest length?  Use the Python length function to compute the answer quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 4)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    ">>> max(dino_vectors, key=length)\n",
    "(6, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Suppose a vector $\\vec{w}$ has coordinates $(2 ,3)$.  What are the approximate coordinates of the scalar multiple $\\pi \\cdot \\vec{w}$?  Draw an approximation of the original vector and the new vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt, pi\n",
    "\n",
    "w = (sqrt(2),sqrt(3))\n",
    "w_scaled = (pi * sqrt(2), pi * sqrt(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.442882938158366, 5.441398092702653)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x493.714 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Arrow(w_scaled, color=red),\n",
    "    Arrow(w, color=black)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Write a python function `scale(s, v)` that multiplies the input vector `v` by the input scalar `s`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale(scalar,v):\n",
    "    return (scalar * v[0], scalar * v[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MINI-PROJECT:** Suppose $\\vec{u} = (-1,1)$ and $\\vec{v} = (1,1)$ and suppose $r$ and $s$ are real numbers.  Specifically, let’s assume $-1 < r < 1$ and $-3 < s < 3$.  \n",
    "\n",
    "Where are the possible points on the plane where the vector $r \\cdot \\vec{u} + s \\cdot \\vec{v}$ could end up?  \n",
    "\n",
    "Note: the order of operations is the same for vectors as it is for numbers: we assume scalar multiplication is carried out first, and then vector addition (unless parentheses specify otherwise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from random import uniform\n",
    "u = (-1,1)\n",
    "v = (1,1)\n",
    "def random_r():\n",
    "    return uniform(-3,3)\n",
    "def random_s(): \n",
    "    return uniform(-1,1)\n",
    "possibilities = [add(scale(random_r(), u), scale(random_s(), v)) \n",
    "                 for i in range(0,500)]\n",
    "draw(\n",
    "    Points(*possibilities)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Write a Python function `subtract(v1,v2)` that returns the result of `v1` minus `v2`, where the inputs and output are tuples of coordinates as we’ve seen so far."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def subtract(v1,v2):\n",
    "    return (v1[0] - v2[0], v1[1] - v2[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Write a Python function `distance(v1,v2)` that returns the distance between two input vectors (noting that the subtract function from the previous exercise already gives the displacement).  \n",
    "\n",
    "Write another Python function `perimeter(vectors)` that takes a list of vectors as an argument and returns the sum of distances from each vector to the next, including the distance from the last vector to the first.  What is the perimeter of the polygon defined by `dino_vectors`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(v1,v2):\n",
    "    return length(subtract(v1,v2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perimeter(vectors):\n",
    "    distances = [distance(vectors[i], vectors[(i+1)%len(vectors)])\n",
    "                    for i in range(0,len(vectors))]\n",
    "    return sum(distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sanity check with a square\n",
    "square = [(1,0),(1,1),(0,1),(0,0)]\n",
    "draw(Polygon(*square), grid=(0.2,0.2), axes=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# should be 1+1+1+1=4\n",
    "perimeter(square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44.77115093694563"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perimeter(dino_vectors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MINI-PROJECT:** Let $\\vec{u}$ be the vector $(1,2)$.  Suppose there is another vector, $\\vec{v}$, with positive integer coordinates $(n, m)$ such that $n > m$, and having distance $13$ from $\\vec{u}$.  What is the displacement from $\\vec{u}$ to $\\vec{v}$?  Hint: you can use Python to search for the vector $\\vec{v}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**SOLUTION:** We only need to search possible integer pairs (n,m) where n is within 13 units of 1 and m is within 13 units of -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(13, 4)\n"
     ]
    }
   ],
   "source": [
    "for n in range(-12,15):\n",
    "    for m in range(-14, 13):\n",
    "        if distance((n,m), (1,-1)) == 13 and n > m > 0:\n",
    "            print((n,m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angles and trigonometry in the plane"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Radians and trigonometry in python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6197751905438615"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import tan\n",
    "tan(45) # tangent of 45 radians, not degrees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999999"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import tan, pi\n",
    "tan(pi/4) # now this is the tangent of pi/4 radians = 45 degrees "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin, cos\n",
    "def to_cartesian(polar_vector):\n",
    "    length, angle = polar_vector[0], polar_vector[1]\n",
    "    return (length*cos(angle), length*sin(angle))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.993177550236464, 3.0090751157602416)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify that 5 units @ 37 degrees takes us to (4,3)\n",
    "angle = 37*pi/180\n",
    "to_cartesian((5,angle))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8414709848078965"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import asin\n",
    "sin(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asin(0.8414709848078965)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9827937232473292"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trying to find an angle with sin = 3/sqrt(13)\n",
    "from math import sqrt\n",
    "asin(3/sqrt(13))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1587989303424644"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import acos\n",
    "acos(-2/sqrt(13))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5547001962252293"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos(2.1587989303424644)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5547001962252291"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-2/sqrt(13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8320502943378436"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(2.1587989303424644)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8320502943378437"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3/sqrt(13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.158798930342464"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import atan2\n",
    "atan2(3,-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_polar(vector):\n",
    "    x, y = vector[0], vector[1]\n",
    "    angle = atan2(y,x)\n",
    "    return (length(vector), angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 0.0)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_polar((1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.605551275463989, 2.158798930342464)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_polar((-2,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Confirm that the vector given by cartesian coordinates (-1.34,2.68) has length approximately 3, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9963310898497184"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length((-1.34,2.68))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** What is $116.57^\\circ$ in radians?  Use Python to compute the tangent of this angle, and confirm that it is close to $-2$ as we saw above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**SOLUTION:** $116.57^\\circ · (1 \\text{rad} / 57.296^\\circ) = 2.035 \\text{rad}.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.9972227673316139"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.035)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Locate the angle $10\\pi/6$.  Do you expect the values of $\\cos(10\\pi/6)$ and $\\sin(10\\pi/6)$ to be positive or negative?  Use Python to calculate their values and confirm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**SOLUTION:** The angle $\\pi/6$ is one third of a quarter-turn, so $10\\pi/6$ is less than a quarter turn short of a full rotation.  This means that it points \"down and to the right\".  The cosine should be positive and the sine should be negative, since distance in this direction corresponds with positive horizontal displacement and negative vertical displacement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.8660254037844386"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(10*pi/6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos(10*pi/6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** The following list comprehension creates 1000 points in polar coordinates.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "polar_coords = [(cos(5*x*pi/500.0), 2*pi*x/1000.0) for x in range(0,1000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python code, convert them to cartesian coordinates, and connect them in a closed loop with line segments to draw a picture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "polar_coords = [(cos(x*pi/100.0), 2*pi*x/1000.0) for x in range(0,1000)]\n",
    "vectors = [to_cartesian(p) for p in polar_coords]\n",
    "draw(Polygon(*vectors, color=green))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Find the angle to get to the point (-2,3) by “guess-and-check”.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.141592653589793, 1.5707963267948966)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we want to make guesses between pi/2 and pi\n",
    "pi, pi/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.286261674628062"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(1.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7470222972386602"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.3738230567687948"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7098465429045078"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5289797578045667"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.4961035416162771"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5124173422757465"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.155)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.50913489938793"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.156)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.505862348872722"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.157)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5025996395625056"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tan(2.158)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.4993467206361923"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we conclude the angle is between 2.158 and 2.159.\n",
    "tan(2.159)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:**  Find another point in the plane with the same tangent as $\\theta$, that is $-3/2$.  Use Python’s implementation of the arctangent function, `math.atan`, to find the value of this angle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import atan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.982793723247329"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "atan(-3/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this is the direction to the point (2,-3).  \n",
    "# tan(-3/2) = tan(-1.5) = tan(3/-2)\n",
    "draw(Arrow((2,-3)), Points((2,-3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Without using Python, what are polar coordinates corresponding to the cartesian coordinates $(1,1)$ and $(1,-1)$?  Once you’ve found the answers, use to_polar to check your work.\n",
    "\n",
    "**SOLUTION:** The answers should be $(\\sqrt{2},\\pi/4)$ and $(\\sqrt{2},-\\pi/4)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.4142135623730951, 0.7853981633974483)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_polar((1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.4142135623730951, -0.7853981633974483)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_polar((1,-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.4142135623730951, 0.7853981633974483)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#compare to\n",
    "(sqrt(2), pi/4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.4142135623730951, -0.7853981633974483)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(sqrt(2), -pi/4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transforming collections of vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rotation_angle = pi/4\n",
    "\n",
    "dino_polar = [to_polar(v) for v in dino_vectors]\n",
    "dino_rotated_polar = [(l,angle + rotation_angle) for l,angle in dino_polar]\n",
    "dino_rotated = [to_cartesian(p) for p in dino_rotated_polar]\n",
    "\n",
    "draw(\n",
    "    Polygon(*dino_vectors, color=gray),\n",
    "    Polygon(*dino_rotated, color=red)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Create a `rotate(angle, vectors)` function which takes an array of input vectors in cartesian coordinates and returns them by the specified angle (counterclockwise or clockwise according to whether the angle is positive or negative). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate(angle, vectors):\n",
    "    polars = [to_polar(v) for v in vectors]\n",
    "    return [to_cartesian((l, a+angle)) for l,a in polars]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combining vector transformations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_dino = translate((8,8), rotate(5 * pi/3, dino_vectors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE:** Create a function `polygon(n)` which returns cartesian coordinates of a regular $n$-sided polygon (that is, having all angles and side lengths equal).  For instance, `polygon(7)` could produce vectors defining a heptagon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regular_polygon(n):\n",
    "    return [to_cartesian((1, 2*pi*k/n)) for k in range(0,n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Polygon(*regular_polygon(7))\n",
    ")"
   ]
  }
 ],
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